An introduction to plotting data
|
|
- Byron Briggs
- 6 years ago
- Views:
Transcription
1 An introduction to plotting data Eric D. Black California Institute of Technology February 25, Introduction Plotting data is one of the essential skills every scientist must have. We use it on a near-daily basis for visualizing our data, drawing conclusions from it, and communicating our results to the rest of the world. In the old days people drew plots by hand, with pen and ink, on graph paper. This was very easy to learn and quick to do, but it was also very limited. If you wanted to make anything more than a minor change to your plot, changing the scale of the axis, for example, or (horrors!) changing it from linear to logarithmic, you basically had to start over and draw a new one. Today we have tools to make all these tasks, as well as the analysis of our data, much easier, and there is no better time than now for you to start learning them. This week we are going to start learning the basics of plotting and analyzing data, but I m going to deviate from the usual way this is taught in most freshman-level courses. Many of you have come to this class with some background in research and already know how to generate plots using a particular software package. Others will be entirely new to the subject. Of those who already have some skill, moreover, the particular software you know how to use will vary widely. For this reason, I m not going to mandate a one-size-fits-all approach. Instead, I m going to focus on what to plot more than on how to do the plotting, and I m going to let you choose what program to do it in. Along with this handout you should also have a second one describing how to do the exercises in Kaleidagraph, and that is the program I recommend you use if you are new to the subject. If you are already fluent in another program and want to use that, you are free to do so. 1
2 2 Single-variable plots Here, we will focus on two-dimensional plots of single-variable data. For the purposes of our discussion, let s assume you have a set of data points of the form, {x i, y i } where i runs from 1 to N, the total number of data points. Moreover, let s assume you suspect there is a connection between the numbers, i.e. that y i depends on x i somehow. In this context, x i is called the independent variable and is the one you can control. You have a knob, for example, that allows you to set a particular value for x i at will, and then measure the outcome of some experiment that that is connected to it. This outcome is y i, and we will call this the dependent variable because it is dependent on x i. The obvious thing you will want to do is plot a graph of y i vs. x i. This graph will be more than a simple illustration. As Edward Tufte points out [1], At their best, graphics are instruments for reasoning about quantitative information. Often the most effective way to describe, explore, and summarize a set of numbers - even a very large set - is to look at pictures of those numbers. LABORATORY EXERCISE 1: Import the following data set into your program, and make a plot of y vs. x. 2
3 X Y If you don t want to type it in by hand, you can download it at phy003/labs/data1.txt 2.1 How to do this in kaleidagraph To reiterate, you don t have to use Kaleidagraph to do these exercises. This section is optional. If you would rather use another program you are free to do so, whether on your own computer or one of the lab s. I am including these instructions because I think Kaleidagraph is the easiest to pick up in a short period of time and carries with it the least amount of frustration for a beginner. (There is some level of frustration in all of them.) It is also a fullfeatured tool that any experimentalist - physicist, biologist, etc. - can use at any stage of his or her career to generate just about any publication-quality plot you need. 3
4 This is what the Kaleidagraph icon looks like. If you are using one of the imacs in the lab, it should already be in the dock. After it starts up, you should see two windows, one for data entry and another for forumla entry. (If one of these does not show up, go to the Windows menu in the menu bar and choose Show Data or Formula Entry to make it appear.) At this point you can type your data into the cells of the data window, or you can open an existing data file. Figure 1: How to open a data file in kaleidagraph. After you choose Open from the File menu, a dialog box will appear that allows you to choose the file you want to open. 4
5 Figure 2: The dialog box for choosing a file to open. Figure 3: Once you have chosen the file to open, another dialog box appears allowing you to specify how it s read. Most of these are self-explanatory. Note the option to read the first line of data as column titles. 5
6 Figure 4: The data looks like this once you have opened it. Note how the titles for the columns are preserved, if you choose that option. 6
7 Figure 5: To make a plot, pull down the Gallery menu and choose the type you want. For a set of discrete data points, Scatter (under the Linear submenu) is a good choice. Figure 6: Once you have chosen the type of plot you want, a dialog box will come up to set which column to use as the X and Y axis. Click the appropriate buttons, and then click New Plot. 7
8 Figure 7: And here is the result. 8
9 3 Error bars You should have started on your reading from Taylor by now, and you have probably even done the first homework set. That is your introduction to uncertainty and what it means, so I am not going to go over that material again here. This section is about how to graphically represent your uncertainty on your plot with error bars, little lines above and below your data points whose lengths show to the uncertainty in the data point itself. Any decent software will allow you to put error bars on your data points, and it should also allow you to specify them any way you want. LABORATORY EXERCISE 2: Put error bars on your plot. Use σ = 0.33 for the uncertainty in the Y value of each point. 3.1 How to do this in Kaleidagraph Pull down the Plot menu, and from it choose the Error Bars... option. If this is greyed out, click on your plot window and then try again. Follow the instructions from there. 9
10 Figure 8: To put error bars on your data points, pull down the Plot menu, and choose Error Bars. This will pull up a dialog box allowing you to specify whether to put them on the X or Y values (horizontal or vertical), and then a second dialog box allowing you to specify what their values should be. 10
11 Figure 9: And the result. 11
12 4 Comparison with a theory curve Very often you want to plot a theory curve along with your data and see how well the two agree. All modern software will include an automatic routine that will do this for you, but before you haul off and click that button, I want you to understand how it works. I don t want it to be a black box for you. LABORATORY EXERCISE 3: Estimate the slope and y-intercept of a line that passes through these data points. Use the form f(x) = Ax + B and add this line to your plot. agreement looks good. Adjust A and B as necessary until the 4.1 How to do this in Kaleidagraph Create a new data window by selecting New from the File menu. Figure 10: Open a new data window. This is where you will generate the data for your theory curve. 12
13 Click the top of the first column to highlight it, then pull down the Functions menu, and select Create Series. Figure 11: Highlight the first column, then pull down the Functions menu and select Create Series. You can create a series with any resolution you want. A hundred points with a spacing of 0.1 will work fine for our purposes. Now click on the Formula Entry window, and type in the theoretical formula you want to use to generate your theory curve. This uses a standard spreadsheet-style notation, where the first column is column zero or c0, the second is c1, etc. Figure 13 shows how we would write our f(x) = Ax + B, with guesses of 0.5 for the slope A and 3.5 for the y-intercept B. Formula entry is really very powerful and is almost a full scripting language. We will just be doing basic things with it here. A full treatment of it is beyond the scope of this lab, but you should be aware that it has a great deal of capabilities. 13
14 Figure 12: Setting the parameters of the series. Figure 13: Defining a formula for your theory curve. In this case it is f(x) = Ax + B, where x is the series we defined in the first column, labelled c0, the slope A is set at 0.5, and the y-intercept B is 3.5. (Yes, you can define variables. No, I don t want to get into that here.) The output is saved in the second column, which Kaleidagraph recognizes as c1. Click Run when you are done. 14
15 Figure 14: Running your function populates c1 with the result of applying your function to the series in c0. Figure 15: To add your newly-generated theory curve to your plot, first click on your plot, then go back to the Gallery menu, and choose Scatter again. 15
16 Figure 16: You can use data from many different Data windows for multiple curves on the same plot. Note the pull-down menu that says Data 3. You can select columns from as many data windows as you have to add to your plot, and define whichever you want to be the X and Y variables. 16
17 Figure 17: And this is what you should get. (In some cases, adding a theory curve will remove your error bars. If this happens to you, just regenerate them.) At this point the y-intercept looks pretty good, but obviously our initial guess for the slope was too small. Tweak the parameters, and regenerate the plot until the fit looks right. 17
18 5 Residuals One way to judge how well a theory curve fits your data is to plot your residuals, the difference between the data and the theory for each point, along with the error bars. R i = y i f(x i ) The error bars on R i are the same as those on y i. If you ve gotten that far in Taylor, this is because the error on f(x i ) is essentially negligible. LABORATORY EXERCISE 4: Calculate and plot your residuals, with error bars. 5.1 Kaleidagraph You know enough now to be able to do this without me walking you through it. (There are actually several different ways of doing it, all equally valid.) You should get something that looks like this. 18
19 Figure 18: Residuals with error bars. 6 χ 2 test Up to now you have been just looking at your plot and judging by eye whether or not the fit looked right. Now we need a quantitative measure of how good the agreement between your theory curve and data points is. The standard way to do that is with a quantity called the reduced Chi squared, or χ 2 r. You will see more of this in your Taylor homework, but for now we will simply define it as the mean-squared deviation of the data points from the theory curve, measured in units of the error bars. χ 2 r 1 N N (y i f(x i )) 2 (1) i=1 σ 2 The distance between a data point and a theory curve that fits its set 19
20 should be on the order of the uncertainty σ, so the reduced chi squared should be around one for a curve that fits the data. If its value is much greater than one, that usually means that the theory is way off from the data. I say usually because it is also possible to get a large χ 2 by underestimating your error bars, but that seldom happens to careful scientists. More often than not, if you make a mistake in estimating your error bars, you do so by assuming they are bigger than they really are. This makes your χ 2 much less than one. χ 2 is what computers use to do automated fitting of theory curves to data sets. Every theory curve has a certain number of parameters that can be adjusted to change the curve. In our linear case there were two, the slope A and y-intercept B. When you ask a computer to do a curve fit for you, it will just adjust the parameters to minimize the χ 2. (It can do this even if you don t supply error bars, but the value of the final, minimized χ 2 won t necessarily be close to one.) LABORATORY EXERCISE 5: Calculate the reduced chi squared for your best-looking theory curve. Does it indicated a good fit? Does it indicate appropriately-chosen error bars? 6.1 How to do this in Kaleidagraph There are, of course, many ways to do this. The most straightforward way is, 1. Insert two new columns into your data using the Insert Column command from the Data menu. 2. Run your theory function on the X values in your data. 3. Define a formula to calculate the individual terms in the sum in Equation 1, e.g. c3=(c1-c2)ˆ2/(0.33ˆ2), where c1 is the column containing the Y values of your data, and c2 is the column containing theory values you just generated. 4. Sum the terms and divide by the total number of terms (20) by defining a function like this and running it, cell(23,3)=csum(c3)/20 20
21 This will write the result to the cell in the 23rd row and fourth column (well outside of where your data lives), and this will be your chi squared. 7 Least-squares fitting In the case where your theory curve is a straight line, it is simple to calculate the two parameters A and B that minimize χ 2 r and therefore optimize the fit. Our expression for the reduced chi squared (Equation 1) becomes χ 2 r 1 N N (y i Ax i B) 2 i=1 σ 2 To find the parameters A and B that minimize this, we just take the derivatives with respect to A and B, and set them to zero. This gives us and χ 2 r A = 0 and χ2 r B = 0 N (y i Ax i B)x i = 0 i=1 N (y i Ax i B) = 0 i=1 These two equations are easy to solve for A and B, giving us straightforward formulae for the optimal coefficients. A = ( ) ( ) N N N N x i y i x i y i i=1 i=1 i=1 ( ) N N N 2 (2) x 2 i x i i=1 i=1 and B = ( ) ( ) ( ) ( ) N N N N x 2 i y i x i x i y i i=1 i=1 i=1 i=1 ( ) N N N 2 (3) x 2 i x i i=1 i=1 21
22 This is known as least-squares fitting because it finds the parameters that produce the minimum value for the chi squared. (The careful reader may have noted that I have gone back to using an equals sign = where I had been using an approximately-equals sign before. That s because the approximation was in the 1/N term in front of the sum, which does not matter for zeroing the derivative.) LABORATORY EXERCISE: Using Equations 2 and 3, calculate the parameters A and B for your data. How close are they to the ones you estimated in Section 4? 7.1 More general cases This procedure can be extended to any theoretical function that is a linear combination of individual functions. The usual example is a polynomial of order n. f(x) = a 0 + a 1 x + a 2 x a n x n Minimizing the chi squared between this function and a set of data points would yield a set of n + 1 linear equations, which can be treated by matrix methods to find the parameters a 0, a 1, etc. Note that the terms do not have to be polynomials, only a linear combination of things, so the procedure would work just as well for a function of the form f(x) = A sin(2πx) + Be x + C ln(x) where the parameters to be adjusted for the fit are A, B, and C. The procedure only breaks down if one of your fit parameters falls inside the argument of one of your nonlinear functions. For cases like that more sophisticated methods exist, but you already learned the most basic one in Section 4: adjust the parameters by hand until the fit appears to be a good one. That procedure is often referred to as chi-by-eye, and good experimentalists use it far more than they will usually admit. 8 Automated fitting Remember how I told you I didn t want you using the curve fitting routines built into the software just yet? Well, now you know enough to understand how they work. Try it out, and see what happens. 22
23 LABORATORY EXERCISE 6: Using the built-in curve-fitting routine in your software, fit a line to your data, and see how the slope and intercept compare with your own estimates. 8.1 How to do this in Kaleidagraph Curve fitting in Kaleidagraph is very straightforward. Figure 19: To add a curve fit to your plot, click on the plot you want to fit, then pull down the Curve Fit menu, and choose the type of fit you want. In this case, it is Linear. 23
24 Figure 20: The result is what you expect, and the fitted formula is printed on the plot. The R is a correlation coefficient, which, like χ 2, serves as a measure of the goodness of the fit. References [1] Edward R. Tufte, The Visual Display of Quantitative Information, Graphics Pr; 2nd edition (2001). 24
25 A How to plot and fit data in Microsoft Excel Microsoft Excel is ubiquitous. You have probably used it before. You probably already have it on your computer, or at least something compatible with it like Open Office. And finally, you will probably see it again after you leave this class. For these reasons you may decide to plot your data in Excel, and that is why I am including this appendix. All of the following examples were done in the 2011 version of Excel on a Macintosh. A.1 How to open a data file in Microsoft Excel Choose Open from the File menu. A dialog box will appear where you specify the location of the file. After you specify the file, three more dialog boxes will come up in succession, allowing you to specify how the file is to be interpreted, i.e. how the columns are separated (delimited), how the individual entries should be formatted, etc. (Figures 23, 24, and 25). Figure 21: Opening a data file from Microsoft Excel. 25
26 Figure 22: Specifying which file to open. You may have to choose All Readable Documents from the Enable pulldown menu before you can access a plain-text file. Figure 23: The first of three dialog boxes. A.2 How to make a plot Plots are called Charts in Excel. To make one, first select the data you want to plot, as shown in Figure 26. Then, click on the word Charts at the top of the window. The green bar that contains the words Home, Layout, Tables, Charts, etc. is called the Ribbon, and each option in the Ribbon contains a 26
27 Figure 24: The second of three dialog boxes. Figure 25: The third of three dialog boxes. menu of its own. In the Charts menu there is a list of icons grouped together under the heading Insert Chart. These options have pictures associated with them and are largely self-explanatory, and the two that are of interest to us are Line and Scatter. Unfortunately, both have severe limitations. 27
28 Figure 26: What you get. Line plots, as you might expect, connect each data point with a line. This is sometimes useful if you have a lot of data points and aren t planning on marking each with its own little symbol, but it s less than ideal for the kinds of plots you will be making in this lab. Line plots also don t support horizontal error bars, so if you are planning on including those, Line is right out. Scatter plots don t connect the dots with a line from point to point, and they allow vertical and horizontal error bars. However, you don t get the option of one or the other. You must accept both vertical and horizontal error bars. A.3 Adding error bars To add error bars, click on Chart Layout in the ribbon, then follow the directions from there. Excel is a little quirky about this. First of all, it automatically sets your error bars to some value it thinks they should be, so you will have to override this manually. Second, as I mentioned above, your options are somewhat limited. With a scatter plot, you get both vertical and horizontal error bars, whether you want them or not. If you want only vertical error bars, you must choose Line Plot as your style and then put up with the lines that 28
29 Figure 27: Click on the Charts tab in the Ribbon, then select Scatter as the type of plot. Figure 28: This is what you get. 29
30 connect your data points. Figure 29: Click on the Chart Layout tab next to the Charts tab in the Ribbon, then select Error Bars. To specify the value of your error bars, as opposed to letting Excel decide what they should be, go straight to Error Bar Options. 30
31 Figure 30: Even though Excel puts error bars on the independent variable (X), you don t get to specify them yet. Figure 31: To set the X error bars, click on one of the data points in your plot. That will bring up this dialog box, which now contains a tab at the top that will allow you to adjust either the X or the Y error bars. To suppress the X error bars, choose Fixed Value, and set it to zero. 31
32 Figure 32: This is what you get. 32
ENV Laboratory 2: Graphing
Name: Date: Introduction It is often said that a picture is worth 1,000 words, or for scientists we might rephrase it to say that a graph is worth 1,000 words. Graphs are most often used to express data
More informationDealing with Data in Excel 2013/2016
Dealing with Data in Excel 2013/2016 Excel provides the ability to do computations and graphing of data. Here we provide the basics and some advanced capabilities available in Excel that are useful for
More informationExcel Spreadsheets and Graphs
Excel Spreadsheets and Graphs Spreadsheets are useful for making tables and graphs and for doing repeated calculations on a set of data. A blank spreadsheet consists of a number of cells (just blank spaces
More informationPlotting Graphs. Error Bars
E Plotting Graphs Construct your graphs in Excel using the method outlined in the Graphing and Error Analysis lab (in the Phys 124/144/130 laboratory manual). Always choose the x-y scatter plot. Number
More information= 3 + (5*4) + (1/2)*(4/2)^2.
Physics 100 Lab 1: Use of a Spreadsheet to Analyze Data by Kenneth Hahn and Michael Goggin In this lab you will learn how to enter data into a spreadsheet and to manipulate the data in meaningful ways.
More information0 Graphical Analysis Use of Excel
Lab 0 Graphical Analysis Use of Excel What You Need To Know: This lab is to familiarize you with the graphing ability of excels. You will be plotting data set, curve fitting and using error bars on the
More informationThe first thing we ll need is some numbers. I m going to use the set of times and drug concentration levels in a patient s bloodstream given below.
Graphing in Excel featuring Excel 2007 1 A spreadsheet can be a powerful tool for analyzing and graphing data, but it works completely differently from the graphing calculator that you re used to. If you
More information252 APPENDIX D EXPERIMENT 1 Introduction to Computer Tools and Uncertainties
252 APPENDIX D EXPERIMENT 1 Introduction to Computer Tools and Uncertainties Objectives To become familiar with the computer programs and utilities that will be used throughout the semester. You will learn
More informationChapter 3: Rate Laws Excel Tutorial on Fitting logarithmic data
Chapter 3: Rate Laws Excel Tutorial on Fitting logarithmic data The following table shows the raw data which you need to fit to an appropriate equation k (s -1 ) T (K) 0.00043 312.5 0.00103 318.47 0.0018
More informationaddition + =5+C2 adds 5 to the value in cell C2 multiplication * =F6*0.12 multiplies the value in cell F6 by 0.12
BIOL 001 Excel Quick Reference Guide (Office 2010) For your lab report and some of your assignments, you will need to use Excel to analyze your data and/or generate graphs. This guide highlights specific
More informationUsing Excel for Graphical Analysis of Data
Using Excel for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable physical parameters. Graphs are
More informationExercise: Graphing and Least Squares Fitting in Quattro Pro
Chapter 5 Exercise: Graphing and Least Squares Fitting in Quattro Pro 5.1 Purpose The purpose of this experiment is to become familiar with using Quattro Pro to produce graphs and analyze graphical data.
More informationAdministrivia. Next Monday is Thanksgiving holiday. Tuesday and Wednesday the lab will be open for make-up labs. Lecture as usual on Thursday.
Administrivia Next Monday is Thanksgiving holiday. Tuesday and Wednesday the lab will be open for make-up labs. Lecture as usual on Thursday. Lab notebooks will be due the week after Thanksgiving, when
More informationGraphical Analysis of Data using Microsoft Excel [2016 Version]
Graphical Analysis of Data using Microsoft Excel [2016 Version] Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable physical parameters.
More informationWhy Use Graphs? Test Grade. Time Sleeping (Hrs) Time Sleeping (Hrs) Test Grade
Analyzing Graphs Why Use Graphs? It has once been said that a picture is worth a thousand words. This is very true in science. In science we deal with numbers, some times a great many numbers. These numbers,
More informationExcel Primer CH141 Fall, 2017
Excel Primer CH141 Fall, 2017 To Start Excel : Click on the Excel icon found in the lower menu dock. Once Excel Workbook Gallery opens double click on Excel Workbook. A blank workbook page should appear
More informationHere is the data collected.
Introduction to Scientific Analysis of Data Using Spreadsheets. Computer spreadsheets are very powerful tools that are widely used in Business, Science, and Engineering to perform calculations and record,
More informationUsing Excel for Graphical Analysis of Data
EXERCISE Using Excel for Graphical Analysis of Data Introduction In several upcoming experiments, a primary goal will be to determine the mathematical relationship between two variable physical parameters.
More informationHomework 1 Excel Basics
Homework 1 Excel Basics Excel is a software program that is used to organize information, perform calculations, and create visual displays of the information. When you start up Excel, you will see the
More informationExcel for Gen Chem General Chemistry Laboratory September 15, 2014
Excel for Gen Chem General Chemistry Laboratory September 15, 2014 Excel is a ubiquitous data analysis software. Mastery of Excel can help you succeed in a first job and in your further studies with expertise
More informationPractical 1P1 Computing Exercise
Practical 1P1 Computing Exercise What you should learn from this exercise How to use the teaching lab computers and printers. How to use a spreadsheet for basic data analysis. How to embed Excel tables
More informationSurvey of Math: Excel Spreadsheet Guide (for Excel 2016) Page 1 of 9
Survey of Math: Excel Spreadsheet Guide (for Excel 2016) Page 1 of 9 Contents 1 Introduction to Using Excel Spreadsheets 2 1.1 A Serious Note About Data Security.................................... 2 1.2
More informationError Analysis, Statistics and Graphing
Error Analysis, Statistics and Graphing This semester, most of labs we require us to calculate a numerical answer based on the data we obtain. A hard question to answer in most cases is how good is your
More informationHow to Make Graphs in EXCEL
How to Make Graphs in EXCEL The following instructions are how you can make the graphs that you need to have in your project.the graphs in the project cannot be hand-written, but you do not have to use
More informationSelecting the Right Model Studio - Excel 2007 Version
Name Recitation Selecting the Right Model Studio - Excel 2007 Version We have seen linear and quadratic models for various data sets. However, once one collects data it is not always clear what model to
More informationExcel Tips and FAQs - MS 2010
BIOL 211D Excel Tips and FAQs - MS 2010 Remember to save frequently! Part I. Managing and Summarizing Data NOTE IN EXCEL 2010, THERE ARE A NUMBER OF WAYS TO DO THE CORRECT THING! FAQ1: How do I sort my
More informationMicrosoft Excel Using Excel in the Science Classroom
Microsoft Excel Using Excel in the Science Classroom OBJECTIVE Students will take data and use an Excel spreadsheet to manipulate the information. This will include creating graphs, manipulating data,
More informationReference and Style Guide for Microsoft Excel
Reference and Style Guide for Microsoft Excel TABLE OF CONTENTS Getting Acquainted 2 Basic Excel Features 2 Writing Cell Equations Relative and Absolute Addresses 3 Selecting Cells Highlighting, Moving
More information1 Introduction to Using Excel Spreadsheets
Survey of Math: Excel Spreadsheet Guide (for Excel 2007) Page 1 of 6 1 Introduction to Using Excel Spreadsheets This section of the guide is based on the file (a faux grade sheet created for messing with)
More informationTips and Guidance for Analyzing Data. Executive Summary
Tips and Guidance for Analyzing Data Executive Summary This document has information and suggestions about three things: 1) how to quickly do a preliminary analysis of time-series data; 2) key things to
More informationYour Name: Section: INTRODUCTION TO STATISTICAL REASONING Computer Lab #4 Scatterplots and Regression
Your Name: Section: 36-201 INTRODUCTION TO STATISTICAL REASONING Computer Lab #4 Scatterplots and Regression Objectives: 1. To learn how to interpret scatterplots. Specifically you will investigate, using
More informationDescribe the Squirt Studio
Name: Recitation: Describe the Squirt Studio This sheet includes both instruction sections (labeled with letters) and problem sections (labeled with numbers). Please work through the instructions and answer
More informationLastly, in case you don t already know this, and don t have Excel on your computers, you can get it for free through IT s website under software.
Welcome to Basic Excel, presented by STEM Gateway as part of the Essential Academic Skills Enhancement, or EASE, workshop series. Before we begin, I want to make sure we are clear that this is by no means
More informationMath 2524: Activity 1 (Using Excel) Fall 2002
Math 2524: Activity 1 (Using Excel) Fall 22 Often in a problem situation you will be presented with discrete data rather than a function that gives you the resultant data. You will use Microsoft Excel
More informationMicrosoft Excel 2007 Creating a XY Scatter Chart
Microsoft Excel 2007 Creating a XY Scatter Chart Introduction This document will walk you through the process of creating a XY Scatter Chart using Microsoft Excel 2007 and using the available Excel features
More informationDiode Lab vs Lab 0. You looked at the residuals of the fit, and they probably looked like random noise.
Diode Lab vs Lab In Lab, the data was from a nearly perfect sine wave of large amplitude from a signal generator. The function you were fitting was a sine wave with an offset, an amplitude, a frequency,
More informationMaking Tables and Graphs with Excel. The Basics
Making Tables and Graphs with Excel The Basics Where do my IV and DV go? Just like you would create a data table on paper, your IV goes in the leftmost column and your DV goes to the right of the IV Enter
More informationTo Plot a Graph in Origin. Example: Number of Counts from a Geiger- Müller Tube as a Function of Supply Voltage
To Plot a Graph in Origin Example: Number of Counts from a Geiger- Müller Tube as a Function of Supply Voltage 1 Digression on Error Bars What entity do you use for the magnitude of the error bars? Standard
More informationScientific Graphing in Excel 2013
Scientific Graphing in Excel 2013 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.
More informationExcel Basics Rice Digital Media Commons Guide Written for Microsoft Excel 2010 Windows Edition by Eric Miller
Excel Basics Rice Digital Media Commons Guide Written for Microsoft Excel 2010 Windows Edition by Eric Miller Table of Contents Introduction!... 1 Part 1: Entering Data!... 2 1.a: Typing!... 2 1.b: Editing
More information1. Data Analysis Yields Numbers & Visualizations. 2. Why Visualize Data? 3. What do Visualizations do? 4. Research on Visualizations
Data Analysis & Business Intelligence Made Easy with Excel Power Tools Excel Data Analysis Basics = E-DAB Notes for Video: E-DAB-05- Visualizations: Table, Charts, Conditional Formatting & Dashboards Outcomes
More informationMulti-step transformations
October 6, 2016 Transformations (section 1.6) Day 4 page 1 Multi-step transformations Objective: Apply transformations involving multiple steps or multiple substitutions. Upcoming: We will have a test
More informationExperimental Design and Graphical Analysis of Data
Experimental Design and Graphical Analysis of Data A. Designing a controlled experiment When scientists set up experiments they often attempt to determine how a given variable affects another variable.
More informationDesigned by Jason Wagner, Course Web Programmer, Office of e-learning NOTE ABOUT CELL REFERENCES IN THIS DOCUMENT... 1
Excel Essentials Designed by Jason Wagner, Course Web Programmer, Office of e-learning NOTE ABOUT CELL REFERENCES IN THIS DOCUMENT... 1 FREQUENTLY USED KEYBOARD SHORTCUTS... 1 FORMATTING CELLS WITH PRESET
More informationMicrosoft Excel 2007 Lesson 7: Charts and Comments
Microsoft Excel 2007 Lesson 7: Charts and Comments Open Example.xlsx if it is not already open. Click on the Example 3 tab to see the worksheet for this lesson. This is essentially the same worksheet that
More informationPlease consider the environment before printing this tutorial. Printing is usually a waste.
Ortiz 1 ESCI 1101 Excel Tutorial Fall 2011 Please consider the environment before printing this tutorial. Printing is usually a waste. Many times when doing research, the graphical representation of analyzed
More informationExcel tutorial Introduction
Office button Excel tutorial Introduction Microsoft Excel is an electronic spreadsheet. You can use it to organize your data into rows and columns. You can also use it to perform mathematical calculations
More informationMeeting 1 Introduction to Functions. Part 1 Graphing Points on a Plane (REVIEW) Part 2 What is a function?
Meeting 1 Introduction to Functions Part 1 Graphing Points on a Plane (REVIEW) A plane is a flat, two-dimensional surface. We describe particular locations, or points, on a plane relative to two number
More informationGeology Geomath Estimating the coefficients of various Mathematical relationships in Geology
Geology 351 - Geomath Estimating the coefficients of various Mathematical relationships in Geology Throughout the semester you ve encountered a variety of mathematical relationships between various geologic
More informationFall 2016 CS130 - Regression Analysis 1 7. REGRESSION. Fall 2016
Fall 2016 CS130 - Regression Analysis 1 7. REGRESSION Fall 2016 Fall 2016 CS130 - Regression Analysis 2 Regression Analysis Regression analysis: usually falls under statistics and mathematical modeling
More informationUsing LoggerPro. Nothing is more terrible than to see ignorance in action. J. W. Goethe ( )
Using LoggerPro Nothing is more terrible than to see ignorance in action. J. W. Goethe (1749-1832) LoggerPro is a general-purpose program for acquiring, graphing and analyzing data. It can accept input
More informationHOUR 12. Adding a Chart
HOUR 12 Adding a Chart The highlights of this hour are as follows: Reasons for using a chart The chart elements The chart types How to create charts with the Chart Wizard How to work with charts How to
More information[1] CURVE FITTING WITH EXCEL
1 Lecture 04 February 9, 2010 Tuesday Today is our third Excel lecture. Our two central themes are: (1) curve-fitting, and (2) linear algebra (matrices). We will have a 4 th lecture on Excel to further
More informationIntroduction to the workbook and spreadsheet
Excel Tutorial To make the most of this tutorial I suggest you follow through it while sitting in front of a computer with Microsoft Excel running. This will allow you to try things out as you follow along.
More informationLab 1 Introduction to R
Lab 1 Introduction to R Date: August 23, 2011 Assignment and Report Due Date: August 30, 2011 Goal: The purpose of this lab is to get R running on your machines and to get you familiar with the basics
More information8. MINITAB COMMANDS WEEK-BY-WEEK
8. MINITAB COMMANDS WEEK-BY-WEEK In this section of the Study Guide, we give brief information about the Minitab commands that are needed to apply the statistical methods in each week s study. They are
More informationExperiment 1 CH Fall 2004 INTRODUCTION TO SPREADSHEETS
Experiment 1 CH 222 - Fall 2004 INTRODUCTION TO SPREADSHEETS Introduction Spreadsheets are valuable tools utilized in a variety of fields. They can be used for tasks as simple as adding or subtracting
More informationAdvanced Curve Fitting. Eric Haller, Secondary Occasional Teacher, Peel District School Board
Advanced Curve Fitting Eric Haller, Secondary Occasional Teacher, Peel District School Board rickyhaller@hotmail.com In many experiments students collect two-variable data, make scatter plots, and then
More informationIntroduction to Spreadsheets
Introduction to Spreadsheets Spreadsheets are computer programs that were designed for use in business. However, scientists quickly saw how useful they could be for analyzing data. As the programs have
More informationWe ve been playing The Game of Life for several weeks now. You have had lots of practice making budgets, and managing income and expenses and savings.
We ve been playing The Game of Life for several weeks now. You have had lots of practice making budgets, and managing income and expenses and savings. It is sometimes a challenge to manage a lot of data
More informationIntroduction to Excel Workshop
Introduction to Excel Workshop Empirical Reasoning Center September 9, 2016 1 Important Terminology 1. Rows are identified by numbers. 2. Columns are identified by letters. 3. Cells are identified by the
More informationScientific Graphing in Excel 2007
Scientific Graphing in Excel 2007 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.
More informationUsing Excel This is only a brief overview that highlights some of the useful points in a spreadsheet program.
Using Excel 2007 This is only a brief overview that highlights some of the useful points in a spreadsheet program. 1. Input of data - Generally you should attempt to put the independent variable on the
More informationIntegrated Mathematics I Performance Level Descriptors
Limited A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Integrated Mathematics I. A student at this level has an emerging ability to demonstrate
More informationDOING MORE WITH EXCEL: MICROSOFT OFFICE 2013
DOING MORE WITH EXCEL: MICROSOFT OFFICE 2013 GETTING STARTED PAGE 02 Prerequisites What You Will Learn MORE TASKS IN MICROSOFT EXCEL PAGE 03 Cutting, Copying, and Pasting Data Basic Formulas Filling Data
More informationVIDYA SAGAR COMPUTER ACADEMY. Excel Basics
Excel Basics You will need Microsoft Word, Excel and an active web connection to use the Introductory Economics Labs materials. The Excel workbooks are saved as.xls files so they are fully compatible with
More informationIDS 101 Introduction to Spreadsheets
IDS 101 Introduction to Spreadsheets A spreadsheet will be a valuable tool in our analysis of the climate data we will examine this year. The specific goals of this module are to help you learn: how to
More informationHow to Make Graphs with Excel 2007
Appendix A How to Make Graphs with Excel 2007 A.1 Introduction This is a quick-and-dirty tutorial to teach you the basics of graph creation and formatting in Microsoft Excel. Many of the tasks that you
More informationGraphing on Excel. Open Excel (2013). The first screen you will see looks like this (it varies slightly, depending on the version):
Graphing on Excel Open Excel (2013). The first screen you will see looks like this (it varies slightly, depending on the version): The first step is to organize your data in columns. Suppose you obtain
More informationSPSS Basics for Probability Distributions
Built-in Statistical Functions in SPSS Begin by defining some variables in the Variable View of a data file, save this file as Probability_Distributions.sav and save the corresponding output file as Probability_Distributions.spo.
More informationKaleidaGraph Quick Start Guide
KaleidaGraph Quick Start Guide This document is a hands-on guide that walks you through the use of KaleidaGraph. You will probably want to print this guide and then start your exploration of the product.
More informationYou are to turn in the following three graphs at the beginning of class on Wednesday, January 21.
Computer Tools for Data Analysis & Presentation Graphs All public machines on campus are now equipped with Word 2010 and Excel 2010. Although fancier graphical and statistical analysis programs exist,
More information2 A little on Spreadsheets
2 A little on Spreadsheets Spreadsheets are computer versions of an accounts ledger. They are used frequently in business, but have wider uses. In particular they are often used to manipulate experimental
More informationW7 DATA ANALYSIS 2. Your graph should look something like that in Figure W7-2. It shows the expected bell shape of the Gaussian distribution.
Drawing Simple Graphs W7 DATA ANALYSIS 2 In some experiments, large amounts of data may be recorded and manipulation is performed using computer software. Although sophisticated, specialist software exists
More informationVocabulary Unit 2-3: Linear Functions & Healthy Lifestyles. Scale model a three dimensional model that is similar to a three dimensional object.
Scale a scale is the ratio of any length in a scale drawing to the corresponding actual length. The lengths may be in different units. Scale drawing a drawing that is similar to an actual object or place.
More informationGraphing with Microsoft Excel
Graphing with Microsoft Excel As an AP Physics 1 student, you must be prepared to interpret and construct relationships found in physical laws and experimental data. This exercise is meant to familiarize
More informationINSTRUCTIONS FOR USING MICROSOFT EXCEL PERFORMING DESCRIPTIVE AND INFERENTIAL STATISTICS AND GRAPHING
APPENDIX INSTRUCTIONS FOR USING MICROSOFT EXCEL PERFORMING DESCRIPTIVE AND INFERENTIAL STATISTICS AND GRAPHING (Developed by Dr. Dale Vogelien, Kennesaw State University) ** For a good review of basic
More informationDetailed instructions for video analysis using Logger Pro.
Detailed instructions for video analysis using Logger Pro. 1. Begin by locating or creating a video of a projectile (or any moving object). Save it to your computer. Most video file types are accepted,
More informationMicrosoft Excel 2007
Microsoft Excel 2007 1 Excel is Microsoft s Spreadsheet program. Spreadsheets are often used as a method of displaying and manipulating groups of data in an effective manner. It was originally created
More informationDescribe the Squirt Studio Open Office Version
Name: Recitation: Describe the Squirt Studio Open Office Version Most of this studio is done with a java applet online. There is one problem where you need to carry out a quadratic regression. Unfortunately,
More informationIntroduction to CS graphs and plots in Excel Jacek Wiślicki, Laurent Babout,
MS Excel 2010 offers a large set of graphs and plots for data visualization. For those who are familiar with older version of Excel, the layout is completely different. The following exercises demonstrate
More information1. What specialist uses information obtained from bones to help police solve crimes?
Mathematics: Modeling Our World Unit 4: PREDICTION HANDOUT VIDEO VIEWING GUIDE H4.1 1. What specialist uses information obtained from bones to help police solve crimes? 2.What are some things that can
More informationME 142 Engineering Computation I. Graphing with Excel
ME 142 Engineering Computation I Graphing with Excel Common Questions from Unit 1.2 HW 1.2.2 See 1.2.2 Homework Exercise Hints video Use ATAN to find nominal angle in each quadrant Use the AND logical
More informationIntro To Excel Spreadsheet for use in Introductory Sciences
INTRO TO EXCEL SPREADSHEET (World Population) Objectives: Become familiar with the Excel spreadsheet environment. (Parts 1-5) Learn to create and save a worksheet. (Part 1) Perform simple calculations,
More informationActivity Graphical Analysis with Excel and Logger Pro
Activity Graphical Analysis with Excel and Logger Pro Purpose Vernier s Logger Pro is a graphical analysis software that will allow you to collect, graph and manipulate data. Microsoft s Excel is a spreadsheet
More informationActivity: page 1/10 Introduction to Excel. Getting Started
Activity: page 1/10 Introduction to Excel Excel is a computer spreadsheet program. Spreadsheets are convenient to use for entering and analyzing data. Although Excel has many capabilities for analyzing
More informationRelease notes for StatCrunch mid-march 2015 update
Release notes for StatCrunch mid-march 2015 update A major StatCrunch update was made on March 18, 2015. This document describes the content of the update including major additions to StatCrunch that were
More informationGraphing by. Points. The. Plotting Points. Line by the Plotting Points Method. So let s try this (-2, -4) (0, 2) (2, 8) many points do I.
Section 5.5 Graphing the Equation of a Line Graphing by Plotting Points Suppose I asked you to graph the equation y = x +, i.e. to draw a picture of the line that the equation represents. plotting points
More informationExcel: Tables, Pivot Tables & More
Excel: Tables, Pivot Tables & More February 7, 2019 Sheldon Dueck, MCT dueck21@gmail.com http://bit.ly/pivottables_fmi (Booklet) 1 Contents Tables... 3 Different ways of creating pivot tables... 4 Compact,
More informationLab1: Use of Word and Excel
Dr. Fritz Wilhelm; physics 230 Lab1: Use of Word and Excel Page 1 of 9 Lab partners: Download this page onto your computer. Also download the template file which you can use whenever you start your lab
More informationMath 1525: Lab 4 Spring 2002
Math 1525: Lab 4 Spring 2 Modeling---Best Fit Function: In this lab we will see how to use Excel to find a "best-fit equation" or model for your data. Example: When a new motion picture comes out, some
More informationCreating a Basic Chart in Excel 2007
Creating a Basic Chart in Excel 2007 A chart is a pictorial representation of the data you enter in a worksheet. Often, a chart can be a more descriptive way of representing your data. As a result, those
More informationExcel 2. Module 3 Advanced Charts
Excel 2 Module 3 Advanced Charts Revised 1/1/17 People s Resource Center Module Overview This module is part of the Excel 2 course which is for advancing your knowledge of Excel. During this lesson we
More informationCharts in Excel 2003
Charts in Excel 2003 Contents Introduction Charts in Excel 2003...1 Part 1: Generating a Basic Chart...1 Part 2: Adding Another Data Series...3 Part 3: Other Handy Options...5 Introduction Charts in Excel
More informationPre-Lab Excel Problem
Pre-Lab Excel Problem Read and follow the instructions carefully! Below you are given a problem which you are to solve using Excel. If you have not used the Excel spreadsheet a limited tutorial is given
More informationUsing Microsoft Excel
Using Microsoft Excel Introduction This handout briefly outlines most of the basic uses and functions of Excel that we will be using in this course. Although Excel may be used for performing statistical
More informationDOING MORE WITH EXCEL: MICROSOFT OFFICE 2010
DOING MORE WITH EXCEL: MICROSOFT OFFICE 2010 GETTING STARTED PAGE 02 Prerequisites What You Will Learn MORE TASKS IN MICROSOFT EXCEL PAGE 03 Cutting, Copying, and Pasting Data Filling Data Across Columns
More informationAppendix B: Using Graphical Analysis
Appendix B: Using Graphical Analysis Graphical Analysis (GA) is a program by Vernier Software. This program is loaded on all of the Physics 170A computers as well as all of the regular Physics 170 computers.
More informationMIS 0855 Data Science (Section 006) Fall 2017 In-Class Exercise (Day 18) Finding Bad Data in Excel
MIS 0855 Data Science (Section 006) Fall 2017 In-Class Exercise (Day 18) Finding Bad Data in Excel Objective: Find and fix a data set with incorrect values Learning Outcomes: Use Excel to identify incorrect
More informationMicrosoft Excel: More Tips, Tricks & Techniques. Excel 2010 & Excel Cutting Edge Chapter of IAAP
Microsoft Excel: More Tips, Tricks & Techniques Excel 2010 & Excel 2007 Cutting Edge Chapter of IAAP Dawn Bjork Buzbee, MCT The Software Pro Microsoft Certified Trainer Bonus Resources Follow-up Q&A, additional
More information